two resistors, r1 and r2, are connected in parallel. r1 = 35.0 ohms, and the equivalent resistance of the…

Explanation:

Step1: Recall parallel - resistance formula

The formula for the equivalent resistance $R_{eq}$ of two resistors $R_1$ and $R_2$ in parallel is $\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}$.

Step2: Rearrange the formula to solve for $R_2$

We can rewrite the formula as $\frac{1}{R_2}=\frac{1}{R_{eq}}-\frac{1}{R_1}$. Then $R_2=\frac{1}{\frac{1}{R_{eq}}-\frac{1}{R_1}}$.

Step3: Substitute the given values

Given $R_1 = 35.0\ \Omega$ and $R_{eq}=14.5\ \Omega$. First, calculate $\frac{1}{R_{eq}}-\frac{1}{R_1}=\frac{1}{14.5}-\frac{1}{35.0}$. $\frac{1}{14.5}-\frac{1}{35.0}=\frac{35.0 - 14.5}{14.5\times35.0}=\frac{20.5}{14.5\times35.0}$. Then $R_2=\frac{14.5\times35.0}{20.5}$. $R_2=\frac{507.5}{20.5}=24.756\ \Omega\approx24.8\ \Omega$.

Answer:

$24.8$ ohm